Question

A spring balance has a scale that reads from $0$ to $50kg$. The length of the scale is $20cm$. A body suspended from this balance, when displaced and released, oscillates with period of $0.6s$. What is the weight of the body ?

Answer 1

Maximum mass that the scale can read, $M=50kg$
Maximum displacement of the spring = Length of the scale, $l=20cm=0.2m$
Time period, $T=0.6s$
Maximum force exerted on the spring, $F=Mg$
where,
$g=$ acceleration due to gravity $=9.8m/s^2$

$F=50\times 9.8=490$

$\therefore$ Spring constant, $k=F/l=490/0.2=2450N{m}^{-1}$

Mass m, is suspended from the balance.

Times period, $t=2\pi \sqrt{\frac{m}{k}}$

$\therefore m={\left(\frac{T}{2\pi }\right)}^2\times k={\left(\frac{0.6}{2\times 3.14}\right)}^2\times 2450=22.36kg$

$\therefore$ Weight of the body $=mg=22.36\times 9.8=219.16N$
Hence, the weight of the body is about 219 N.